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Common Core Mathematics in a PLC at Work™, Grades 6–8
This teacher guide illustrates how to sustain successful implementation of the Common Core State Standards for mathematics, grades 6–8. Discover what students should learn and how they should learn it at each grade level. Comprehensive research-affirmed analysis tools and strategies will help you and your collaborative team develop and assess student demonstrations of deep conceptual understanding and procedural fluency.
A Joint Publication With the National Council of Teachers of Mathematics
Benefits
- Discover the five essential paradigm shifts necessary to implement the CCSS for mathematics.
- Receive guidance on forming and sustaining collaborative teams in a Professional Learning Community at Work™ culture.
- Develop a “less is more” content mindset: fewer standards will result in the opportunity of time needed for deeper rigor and conceptual understanding work with students.
- Gain helpful formative assessment strategies for development of student proficiency in the Standards for Mathematical Practice.
- Access dozens of tools, activities, examples, resources, and reproducibles to help teachers and teams analyze, interpret, and implement the Common Core Standards expectations for instruction and assessment.
- Examine the research-affirmed foundation of mathematics content and process standards from 1989 to 2010, and deepen your understanding of the Common Core expectations.
TABLE OF CONTENTS
Chapter 1: Using High-Performing Collaborative Teams for Mathematics
Chapter 2: Implementing the Common Core Standards for Mathematical Practice
Chapter 3: Implementing the Common Core Mathematics Content in Your Curriculum
Chapter 4: Implementing the Teaching-Assessing-Learning Cycle
Chapter 5: Implementing Required Response to Intervention
Epilogue: Your Mathematics Professional Development Model
Appendix A: Standards for Mathematical Practice
Appendix B: Standards for Mathematical Content, Grade 6
Appendix C: Standards for Mathematical Content, Grade 7
Appendix D: Standards for Mathematical Content, Grade 8
PRINTABLE REPRODUCIBLES
Chapter 1
- Figure 1.1: Setting Middle School Teacher Team Collective Commitments Protocol
- Figure 1.2: Sample Team-Meeting Agenda
- Figure 1.3: Sample Team-Meeting Minutes
- Figure 1.4: Options for Scheduling Teacher Collaboration Time
- Figure 1.5: How to Read the CCSS for Mathematics
- Figure 1.6: High-Leverage Activities of Grades 6–8 Grade-Level and Course-Level Collaborative Teams
- Table 1.1: The Seven Stages of Teacher Collaboration Diagnostic Tool
Extending My Understanding
- The Five Disciplines of PLC Leaders
- All Things PLC
- The Educator's PLN
- The Center for Comprehensive School Reform and Improvement
- Tools for Coaches
- Tools for Principals & Administrators
- Learning Forward
- National Council of Supervisors of Mathematics
- The Mathematics Common Core Toolbox
- Chicago Lesson Study Group
- STEM Teachers in Professional Learning Communities: A Knowledge Synthesis
- Learning by Doing: A Handbook for Professional Learning Communities at Work™
Chapter 2
- Figure 2.3: Seven Planning Questions That Promote CCSS Mathematical Practice 1
- Figure 2.4: Sample Geometry Problem—Rectangular Fencing Task
- Table 2.1: Factors Associated With the Maintenance or Decline of High-Level-Cognitive Demand
- Figure 2.6: Sample Problem for Mathematical Practice 2—Verizon Wireless
- Figure 2.7: Sample Integers Task
- Figure 2.10: Sample Middle School Mathematical Modeling Problem—Wikipedia Claim
- Figure 2.12: Student Computational Options Model
- Figure 2.13: Sample Probability Models
- Figure 2.16: CCSS Mathematical Practices Lesson-Planning Tool
- Table 2.2: Elements of an Effective Middle School Mathematics Classroom Lesson Design
Extending My Understanding
- Common Core Implementation Video Series
- Common Core Look-Fors
- Mathematical Practices Learning Community Templates
- Standards for Mathematical Practice
- Common Core State Standards Materials Analysis Tools
- Illustrative Mathematics
- Common Core Standards for Mathematics
- Doing What Works
Chapter 3
- Figure 3.1: How to Read the Grade-Level Standards
- Figure 3.3: Understanding Division Involving Zero
- Figure 3.14: Sample Pacing Calendar
- Figure 3.15: Curriculum Materials Analysis Rubrics
- Figure 3.16: Recommended Honors Sequence
- Table 3.1: CCSS Content Domains by Grade Band
- Table 3.2: CCSS Content Domains and Clusters by Grade, With Emphasis on Grades 6–8
- Table 3.3: Analysis Tool for Grade 7—Ratios and Proportional Relationships (7.RP) Domain
- Table 3.4: Analysis Tool for Grade 6—The Number System (6.NS) Domain
- Table 3.5: Analysis Tool for Grades 6 and 7—Ratios and Proportional Relationships (6.RP and 7.RP) and Grade 8 Functions (8.F) Domains
- Table 3.6: Analysis Tool for Grade 8—Expressions and Equations (8.EE) Domain
- Table 3.7: Analysis Tool for Grade 8—Geometry (8.G) Domain
- Table 3.8: Analysis Tool for Grade 7—Statistics and Probability (7.SP) Domain
Extending My Understanding
- CCSS Mathematics Curriculum Materials Analysis Project
- Illustrative Mathematics
- National Council of Supervisors of Mathematics
- National Council of Teachers of Mathematics Illuminations
- Progressions Documents for the Common Core Math Standards
Chapter 4
- Figure 4.1: The PLC Teaching-Assessing-Learning Cycle
- Figure 4.4: Task Anticipation Sheet
- Figure 4.6: Assessment Instrument Quality—Evaluation Tool
- Figure 4.7: Formative Assessment Strategies for Student Action
- Figure 4.8: Student Action and Commitment for Focused Improvement
- Figure 4.9: Task Analysis Sheet
- Figure 4.10: A Collaborative Team Analysis of Grading Practice
- Table 4.1: Reteaching Versus Re-Engagement Lessons
Extending My Understanding
- Math Common Core Coalition
- The Mathematics Assessment Project
- Partnership for Assessment of Readiness for College and Careers
- Smarter Balanced Assessment Consortium
- Public Lessons: Numerical Patterning
- Silicon Valley Mathematics Initiative
- Re-Engagement Protocol
- Classroom Video Visits
Chapter 5
- Figure 5.1: Equity Reflection Questions
- Figure 5.2: R2TI in Support of the PLC Teaching-Assessing-Learning Cycle
- Table 5.1: Equity Reflection Activity
- Table 5.2: High-Quality Data Checklist
- Table 5.3: Tool for Your Differentiated Response to Learning
Extending My Understanding
- Introduction to the Classroom-Focused Improvement Process
- Mathematics Assessment Project
- National Council of Supervisors of Mathematics
- Math Reasoning Inventory
- National Center on Response to Intervention
- RTI Action Network: Middle School Resources
- Solution Tree RTI Books and Reproducibles
- TODOS: Mathematics for ALL
- Understanding Language
Epilogue
Additional Resources
- Analysis Tool for Grade 6—Expressions and Equations (6.EE) Domain
- Analysis Tool for Grade 6—Geometry (6.G) Domain
- Analysis Tool for Grade 6—Statistics and Probability (6.SP) Domain
- Analysis Tool for Grade 6—Ratios and Proportional Relationships (6.RP) Domain
- Analysis Tool for Grade 7—Expressions and Equations (7.EE) Domain
- Analysis Tool for Grade 7—Geometry (7.G) Domain
- Analysis Tool for Grade 7—The Number System (7.NS) Domain
- Analysis Tool for Grade 7—Ratios and Proportional Relationships (7.RP) Domain
- Analysis Tool for Grade 8—Functions (8.F) Domain
- Analysis Tool for Grade 8—The Number System (8.NS) Domain
- Analysis Tool for Grade 8—Statistics and Probability (8.SP) Domain
- Appendix E: Changes in Mathematical Standards, 1989–2012
- Table E.1: Mathematics Content—Principles and Standards for School Mathematics and the Common Core State Standards
- Table E.2: CCSS Critical Areas and NCTM Focal Points, Grades 6–8
- Types of Teacher Questions
